For optimizing the vibro-acoustic behavior of vehicle bodies above 400 Hz statistical energy analysis (SEA) has become a common tool in recent years. The application of SEA in the automotive industry was first introduced by R. Lyon, G. Maidanik, “Power Flow between Linearly Coupled Oscillators”, JASA, 34, 1962; and P. Smith, Jr., “Response and Radiation of Structural Modes Excited by Sound”, JASA, 34, 1962.
According to the basic principles of SEA, the stationary average energy E within e.g. a ⅓ octave band with center frequency ωm is given byωmL(ωm)E(ωm)=P(ωm)  (1)
wherein
                    L        =                  [                                                                                          η                    11                                    +                                                            ∑                      j                                        ⁢                                          η                                              1                        ⁢                        j                                                                                                                                          -                                      η                    21                                                                                                                                                            ⋯                                                                                      -                                      η                    12                                                                                                                    η                    22                                    +                                                            ∑                      j                                        ⁢                                          η                                              2                        ⁢                        j                                                                                                                                                                                                      ⋯                                                                    ⋮                                                                                                                          ⋰                                            ⋯                                                                                      -                                      η                                          1                      ⁢                      j                                                                                                  ⋯                                                                                                                                                                η                    jj                                    +                                                            ∑                      j                                        ⁢                                          η                      ij                                                                                                    ]                                    (        2        )            
is the (non-symmetric) SEA matrix consisting of frequency dependent loss factors ηij, which are in fact internal loss factors (ILFs) of the subsystems for i=j and coupling loss factors (CLFs) between the subsystems for i≠j, with P being the vector of excitation input powers to the subsystems.
According to known methods for analyzing and/or optimizing the vibro-acoustical sensitivity or behavior of structures as disclosed e.g. in E. Sarradj, “Bestimmung von Sensitivitäten mit der Statistischen Energieanalyse”, DAGA, Bonn, Feb. 26th-29th 1996”; or N. Lalor and G. Stimpson, “FEM+SEA+OPTIMIZATION=LOW NOISE”, 2nd Int. Conference, “Vehicle Comfort: Ergonomic, Vibrational, Noise and Thermal Aspects”, Bologna, Italy, Oct. 14th-16th 1992; the gradient of energy of a selected subsystem with respect to a certain ILF or CLF represents a measure of how changes in that ILF/CLF will influence subsystem energy. This measure can therefore be conveniently used to e.g. minimize a selected subsystem energy for noise reduction purposes, for example the interior of a vehicle passenger cell, by adjusting the appropriate ILF/CLF parameter(s).
However, up to now all known methods fail to give a correct estimate of such subsystem energy changes in case of large, i.e. more than local, ILF and/or CLF variations since they rely on a numerical model of the energy gradient only.
Therefore, there is a need for a generally practicable method of analyzing the vibro-acoustic optimization potential of a structure, and subsequently optimizing its vibro-acoustic behavior, by means of statistical energy analysis (SEA), which method yields fast and correct results under a variety of operating circumstances.